A substantial body of work has addressed why animals live in groups. However, few studies have described how group-living vertebrates are able to coordinate their actions and make collective decisions crucial if individuals are to maximise the benefits and minimise the costs of grouping. In this thesis, I apply observational, experimental, and theoretical methods to address this paucity of knowledge, using a social primate - chacma baboons (Papio ursinus) - as a model system. Specifically, I investigate three concepts upon which group-living is reliant: information use, coordinated behaviour and leadership. I address each of these concepts in turn. First in the case of information use, I show that the foraging decisions of individual baboons meet the predictions of 'producer- scrounger games' - evolutionary models developed to predict when a social forager should find its own food patch, or join the discovery of a group-mate. I also use a simple theoretical model to show that social information can allow less well-informed members of large groups to reach a correct decision with the same probability as more well-informed members of small groups. Second, in the case of coordinated behaviour, I show that individual state and the environment (both social and ecological conditions) can influence levels of behavioural synchrony in baboons. Moreover, behavioural synchrony in baboon groups was seen to positively influence the behaviour of another species: rock kestrels (Falco rupicolus) derived foraging opportunities by associating with baboons as they travel-forage together in desert vegetation 'flushing' kestrel prey items. Finally, I examined leadership behaviour. I used an experimental design that allowed me to test between two alternate decision-making modes: despotism (i.e. leadership) and democracy (i.e. a majority rule, voting). Baboon group foraging decisions were consistently led by the individual who acquired the most benefits from those decisions, namely the dominant male. Subordinate group members followed the leader despite considerable costs, and follower behaviour was mediated by social ties to the leader.